As far as the rules go, you do not need to be at a location you control just to invent. However, you do need to follow any rules that apply to the card being invented.
Deed- placed on your street per deed rules. The Scientist will not need to be at a location you control to invent the deed.
dude- invented dudes are placed at the same location as the dude inventing it. Per pg 42 in the rulebook. Again, no control is necessary to invent a dude.
improvements- The mad scientist won't need to be at a location you control, but all improvements in the game must be attached to a location/deed you control. So the important part for improvements is where it is going, not who is inventing it.